Maybe another way of putting it is “the information that makes you up remains the same”? As in, it doesn’t matter if one electron is exchanged with another, it’s still the same component? Assuming two things have the same physical properties, it doesn’t matter which one you use. You are not just the objects you consist of, but also the way they are positioned/aligned/etc.
Maybe a bit like binary code/data, if you copy a file then the copy will be able to do the same thing. Though I guess it’s more complex than that, because it all depends on where this data is located, so not only the building blocks but also the context in which they exist matters.